Abstract We prove Li-Yau-Kröger-type bounds for Neumann-type eigenvalues of the biharmonic operator on bounded domains in a Euclidean space. also sharp estimates lower order Steklov problem and Laplacian, which directly implies two Reilly-type inequalities corresponding first nonzero eigenvalue.

E.O. Kiktenko, 2, 3 A.S. Trushechkin, C.C.W. Lim, Y.V. Kurochkin, and A.K. Fedorov 5 Russian Quantum Center, Skolkovo, Moscow 143025, Russia Theoretical Department, DEPHAN, Skolkovo, Moscow 143025, Russia Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia Quantum Information Science Group, Computational Sciences and Engineering Division, Oak Ridge National Labo...

X iv :m at h/ 06 10 74 2v 2 [ m at h. C O ] 2 8 O ct 2 00 6 Clustering of spectra and fractals of regular graphs V. Ejov, J.A. Filar, S.K. Lucas, P. Zograf 1 School of Mathematics and Statistics, University of South Australia, Mawson Lakes SA 5095 Australia 2 Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA 3 St. Petersburg Department of Steklov In...

The infinite matrices in Witten’s vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s = 0 limit. We find that s = 1 eigenfunctions just acquire a p term, and x gets rep...

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...

E.O. Kiktenko, 2, 3 N.O. Pozhar, 3 A.V. Duplinskiy, 4 A.A. Kanapin, 5 A.S. Sokolov, S.S. Vorobey, A.V. Miller, V.E. Ustimchik, M.N. Anufriev, 3 A.S. Trushechkin, R.R. Yunusov, V.L. Kurochkin, Y.V. Kurochkin, and A.K. Fedorov ∗ Russian Quantum Center, Skolkovo, Moscow 143025, Russia Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia Bauman Moscow State Technical...

In this paper we find the asymptotic behavior of the spectral counting function for the Steklov problem in a family of self similar domains with fractal boundaries. Using renewal theory, we show that the main term in the asymptotics depends on the Minkowski dimension of the boundary. Also, we compute explicitly a three term expansion for a family of self similar sets, and a two term asymptotic ...

We give an exact analytic solution of the strong coupling limit of the integral equation which was recently proposed to describe the universal scaling function of high spin operators in N = 4 gauge theory. The solution agrees with the prediction from string theory, confirms the earlier numerical analysis and provides a basis for developing a systematic perturbation theory around strong coupling...